Could you describe what you're trying to do a little more, or post a sketch of what you're looking for? I don't understand the relationship you're trying to draw between the Closest Facility analysis and the Service Area analysis.
When you calculated the closest facility travel times, you were presumably using a network dataset with a travel time cost attribute that determines how long it takes to travel on any given street in the network. The Service Area solver can use the same network dataset and cost attribute. If you create service areas around your Facilities, the resulting polygons should show the area reachable within your 30, 60, and 90 minute break values. If the block group points were within those time limits in your closest facility analysis, they should fall under the service area polygons. However, the service area calculation is completely independent of your closest facility calculation.